Decay of correlations for certain multi-dimensional maps

Abstract

We study the decay of correlations for certain multi-dimensional noninvertible maps which do not necessarily satisfy Renyi's condition (the bounded distortion property) and do not necessarily satisfy the Markov condition on the definite partitions. Our method is based on the technique of Markov approximations which was developed by Chernov. We relate the slowness of the decay of correlations to the singularity of the invariant density which is caused by the lack of hyperbolicity. We also see that it can be described by the distortion property of the distributions of the invariant densities.